Home
Class 11
PHYSICS
Two balls having linear momenta vecp(1)=...

Two balls having linear momenta `vecp_(1)=phati` and `vecp_(2)=-phati, ` undergo a collision in free space. There is no external force acting on the ball. Let `vecp_(1)^(')` and `vecp_(2)^(')` be their final momenta. Which of the following option(s) is (are) NOT ALLOWED for an non zero value of `p,a_(1),a_(2),b_(1),b_(2), c_(1)` and `c_(2).`

A

`vecp_(1)^(')=a_(1)hati+b_(1)hatj+c_(1)hatk, vecp_(2)^(')=a_(2)hati+b_(2)hatj`

B

`vecp_(1)^(')=c_(1)hatk, vecp_(2)^(')+c_(2)hatk`

C

`vecp_(1)^(')=a_(1)hati+b_(1)hatj+c_(1)hatk, vecp_(2)^(')=a_(2)hatib_(2)hatj-c_(2)hatk`

D

`vecp_(1)^(')=a_(1)hati+b_(1)hatj, vecp_(2)^(')=a_(2)hati+b_(1)hatj`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we will apply the principle of conservation of momentum. Let's break down the steps: ### Step 1: Understand the Initial Momentum The initial momenta of the two balls are given as: - \(\vec{p}_1 = p \hat{i}\) - \(\vec{p}_2 = -p \hat{i}\) The total initial momentum of the system is: \[ \vec{p}_{\text{initial}} = \vec{p}_1 + \vec{p}_2 = p \hat{i} - p \hat{i} = 0 \] ### Step 2: Apply Conservation of Momentum Since there are no external forces acting on the system, the total momentum before the collision must equal the total momentum after the collision: \[ \vec{p}_{\text{final}} = \vec{p}_1' + \vec{p}_2' = 0 \] ### Step 3: Analyze the Final Momentum From the conservation of momentum, we have: \[ \vec{p}_1' + \vec{p}_2' = 0 \] This implies: \[ \vec{p}_1' = -\vec{p}_2' \] ### Step 4: Evaluate the Options Now, we will evaluate each option to see which ones are NOT allowed given that \(a_1, a_2, b_1, b_2, c_1, c_2\) are all non-zero. #### Option 1: \[ \vec{p}_1' + \vec{p}_2' = a_1 \hat{i} + a_2 \hat{i} + b_1 \hat{j} + b_2 \hat{j} + c_1 \hat{k} = 0 \] This implies: - \(a_1 + a_2 = 0\) - \(b_1 + b_2 = 0\) - \(c_1 = 0\) Since \(c_1\) cannot be zero (given that all values are non-zero), **Option 1 is NOT allowed**. #### Option 2: \[ c_1 + c_2 = 0 \] This allows for \(c_1 = -c_2\), which is possible even if both are non-zero. Thus, **Option 2 is allowed**. #### Option 3: \[ a_1 + a_2 + b_1 + b_2 + c_1 - c_2 = 0 \] This can be satisfied even if \(a_1, a_2, b_1, b_2, c_1, c_2\) are all non-zero. Thus, **Option 3 is allowed**. #### Option 4: \[ a_1 + a_2 + b_1 + b_2 = 0 \] Here, \(a_1 + a_2\) can be zero if \(a_1 = -a_2\) and \(b_1 + b_2\) can also be zero. However, since \(b_1\) and \(b_2\) cannot both be zero, **Option 4 is NOT allowed**. ### Conclusion The options that are NOT allowed are: - **Option 1** - **Option 4**
To solve the problem, we will apply the principle of conservation of momentum. Let's break down the steps: ### Step 1: Understand the Initial Momentum The initial momenta of the two balls are given as: - \(\vec{p}_1 = p \hat{i}\) - \(\vec{p}_2 = -p \hat{i}\) The total initial momentum of the system is: ...
Promotional Banner

Topper's Solved these Questions

  • CENTRE OF MASS

    CENGAGE PHYSICS ENGLISH|Exercise AR_TYPE|1 Videos

  • CENTRE OF MASS

    CENGAGE PHYSICS ENGLISH|Exercise LC_TYPE|3 Videos

  • CENTRE OF MASS

    CENGAGE PHYSICS ENGLISH|Exercise SCQ_TYPE|12 Videos

  • CALORIMETRY

    CENGAGE PHYSICS ENGLISH|Exercise Solved Example|13 Videos

  • DIMENSIONS & MEASUREMENT

    CENGAGE PHYSICS ENGLISH|Exercise Integer|2 Videos

Similar Questions

Explore conceptually related problems

Let (a_(1),b_(1)) and (a_(2),b_(2)) are the pair of real numbers such that 10,a,b,ab constitute an arithmetic progression. Then, the value of ((2a_(1)a_(2)+b_(1)b_(2))/(10)) is

Let vecp = 3ax^(2) hati - 2(x-1)hatj, q=b(x-1)hati + xhatj and ab lt 0 . Then vecp and vecq are parallel for:

Two dipoles vecP_(1) and vecP_(2) are oriented as shown in the figure. Assuming dipole of dipole moment vecP_(2) to be placed at origin and dipole of moment vecP_(1) is at a distance 'd' from origin then

If two equation a_(1) x^(2) + b_(1) x + c_(1) = 0 and, a_(2) x^(2) + b_(2) x + c_(2) = 0 have a common root, then the value of (a_(1) b_(2) - a_(2) b_(1)) (b_(1) c_(2) - b_(2) c_(1)) , is

Let overset(to)(a) =a_(1) hat(i) + a_(2) hat(j) + a_(3) hat(k) , overset(to)(b) = b_(1) hat(i) +b_(2) hat(j) +b_(3) hat(k) " and " overset(to)(c) = c_(1) hat(i) +c_(2) hat(j) + c_(3) hat(k) be three non- zero vectors such that overset(to)(c ) is a unit vectors perpendicular to both the vectors overset(to)(a ) and overset(to)(b) . If the angle between overset(to)(a) " and " overset(to)(b) is (pi)/(6) then |{:(a_(1),,a_(2),,a_(3)),(b_(1),,b_(2),,b_(3)),(c_(1),,c_(2),,c_(3)):}|^2 is equal to

If the quadratic polynomials defined on real coefficient P(x)=a_(1)x^(2)+2b_(1)x+c_(1) and Q(x)=a_(2)x^(2)+2b_(2)x+c_(2) take positive values AA x in R , what can we say for the trinomial g(x)=a_(1)a_(2)x^(2)+b_(1)b_(2)x+c_(1)c_(2) ?

Let ABC and AB'C be two non-congruent triangles with sides BC=B'C=5, AC=6, and angleA is fixed. If A_(1) and A_(2) are the area of the two triangles ABC and AB'C, then the value of (A_(1)^(2)+A_(2)^(2)-2A_(1)A_(2)cos 2A)/((A_(1)+A_(2))^(2)) is

If the momenta of two particles of a system are given by vecp_(1)=2hati-hatj+3hatk and vecp_(2)=-hati+2hatj-2hatk then calculate the angle made by the direction of motion of the system with positive x-axis.

If a_(1) and a_(2) aare two non- collineaar unit vectors and if |a_(1)+a_(2)|=sqrt(3), ,then value of (a_(1)-a_(2)).(2a_(1)-a_(2)) is

If a_(1) and a_(2) are two non- collinear unit vectors and if |a_(1)+a_(2)|=sqrt(3), ,then value of (a_(1)-a_(2)).(2a_(1)-a_(2)) is